Ohio State University Algebraic Geometry Seminar 

  Year 2017-2018

Time: Tuesdays 3-4pm
Location: MW 154

Schedule of talks:


 

TIME  SPEAKER TITLE
August 29  
Tue, 3pm 
Dave Anderson 
(OSU) 
Determinantal formulas for degeneracy loci and Brill-Noether theory
September 5  
Tue, 3pm 
Hsian-Hua Tseng 
(OSU) 
On the quantum K-rings of flag varieties of type A
September 12  
Tue, 3pm 
Angelica Cueto 
(OSU) 
Tropical geometry of genus 2 curves
September 19  
Tue, 3pm 
Herb Clemens 
(OSU) 
Eliptically-fibered Calabi-Yau (CY) threefolds and fourfolds in string theory
October 3  
Tue, 3pm 
Seth Baldwin 
(UNC) 
Positivity in T-equivariant K-theory of flag varieties associated to Kac-Moody groups
October 10  
Tue, 3pm 
TBA 
() 
TBA
October 17  
Tue, 3pm 
Roi Docampo 
(Oklahoma) 
TBA
October 24  
Tue, 3pm 
TBA 
() 
TBA
October 26  
Thu, 4:10pm
CH 240
Renzo Cavalieri 
(Colorado State U.) 
Colloquium talk
October 31  
Tue, 3pm 
Christin Bibby 
(U. Michigan) 
TBA
November 7  
Tue, 3pm 
Chris Manon 
(U. Kentucky) 
TBA
November 14  
Tue, 3pm 
Daniel Litt 
(Columbia U.) 
TBA
November 21  
Tue, 3pm 
TBA 
() 
TBA
November 28  
Tue, 3pm 
Jose Gonzalez 
(UC Riverside) 
TBA
December 5  
Tue, 3pm 
Matthew Satriano 
(U. Waterloo) 
TBA
January 9  
Tue, 3pm 
TBA 
( ) 
TBA
January 16  
Tue, 3pm 
TBA 
() 
TBA
January 23  
Tue, 3pm 
William Fulton* 
(Michigan) 
(*to be confirmed)
January 30  
Tue, 3pm 
TBA 
() 
TBA
February 6  
Tue, 3pm 
TBA 
() 
TBA
February 13  
Tue, 3pm 
TBA 
() 
TBA
February 20  
Tue, 3pm 
TBA 
() 
TBA
February 27  
Tue, 3pm 
TBA 
() 
TBA
March 6  
Tue, 3pm 
TBA 
() 
TBA
March 13  
Tue, 3pm 
(break)  
 
March 20  
Tue, 3pm 
TBA 
() 
TBA
March 27  
Tue, 3pm 
TBA 
() 
TBA
April 3  
Tue, 3pm 
TBA 
() 
TBA
April 10  
Tue, 3pm 
TBA 
() 
TBA
April 16-18  
Tue, 4:10pm
CH 240
Sergey Fomin 
(U. Michigan) 
Zassenhaus Lecture Series 2018
April 24  
Tue, 3pm 
TBA 
() 
TBA

Abstracts


(Anderson): Relations between degeneracy loci and divisors on curves go back over a hundred years: Giambelli's formula for the class of the locus where a matrix drops rank is a cornerstone of Schubert calculus; Brill and Noether's estimate for the dimension of the space of special divisors on a curve also comes from considerations of degeneracy loci. In this talk, I will describe work with Linda Chen and Nicola Tarasca which connects more recent developments in Schubert calculus with formulas by Eisenbud-Harris, Pirola, and Chan-Lopez-Pflueger-Teixidor for the genus of a Brill-Noether curve.


(Tseng): The quantum K-ring of a smooth projective variety X, introduced by Givental and YP Lee, is a deformation of the Grothendieck ring of coherent sheaves on X defined using holomorphic Euler characteristics on moduli spaces of stable maps to X (these are K-theoretic version of Gromov-Witten invariants). In this talk we discuss some properties of the quantum K-rings of X=Flr+1, the variety of complete flags in Cr+1, including:

(1) a presentation of the quantum K-ring;

(2) finiteness of quantum product;

(3) canonical polynomial representatives of Schubert classes.

This is based on joint work in progress with David Anderson and Linda Chen.


(Cueto): In this talk, I will discuss the structure of tropical and non-Archimedean analytic genus 2 curves and their moduli from three perspectives:

(1) as 2-to-1 covers of P1 branched at 6 points;

(2) as solutions to the hyperelliptic equation y2=f(x), where f has degree 5; and

(3) as metric graphs dual to genus 2 nodal algebraic curves over a valued field.

Our first description allows us to give an explicit combinatorial rule to characterize each such metric graph together with a harmonic map to a metric tree on 6 leaves, in terms of the valuations of 6 branch points in P1. Even though the tropicalization of a plane hyperelliptic curve shows no genus, we provide explicit re-embeddings of the input planar hyperelliptic curve that reveals the correct metric graphs.

From our third viewpoint, we consider the moduli space of abstract genus two tropical curves and translate the classical Igusa invariants characterizing isomorphism classes of genus two algebraic curves into the tropical realm. While these tropical Igusa functions do not yield coordinates on the tropical moduli space, we propose an alternative set of invariants that provides new length data. This is joint work with Hannah Markwig.


(Clemens): The talk will construct one example of the `equivalence' between an elliptically-fibered CY-threefold endowed with a semi-stable E8 + E8 bundle and a semi-stable degeneration of an elliptically-fibered CY-fourfold. I will then loosely describe how this equivalence is used to `break' the SU(5)-symmetry of grand unified theory (GUT) to the SU(3)xSU(2)xU(1)-symmetry of what physicists call the Standard Model of the physics of our cosmos.


(Baldwin): The cohomology ring of flag varieties has long been known to exhibit positivity properties. One such property is that the structure constants of the Schubert basis with respect to the cup product are non-negative. Brion (2002) and Anderson-Griffeth-Miller (2011) have shown that positivity extends to K-theory and T-equivariant K-theory, respectively. In this talk I will discuss recent work (joint with Shrawan Kumar) which generalizes these results to the case of Kac-Moody groups.


(Docampo):


(Bibby):


(Manon):


(Litt):


(Gonzalez):


(Satriano):


(Fulton):



Past Seminars

Ohio State University Algebraic Geometry Seminar-Year 2016-2017

Ohio State University Algebraic Geometry Seminar-Year 2015-2016

Ohio State University Algebraic Geometry Seminar-Year 2014-2015

Ohio State University Algebraic Geometry Seminar-Year 2013-2014


This page is maintained by Angie Cueto and Dave Anderson.